MARKOV SWITCHING DYNAMIC REGRESSION MODEL: APPLICATION TO FINANCIAL DATA

ROSEMARY UKAMAKA OKAFOR; JOSEPHINE NNEAMAKA ONYEKA-UBAKA

ROSEMARY UKAMAKA OKAFOR DEPARTMENT OF STATISTICS, UNIVERSITY OF LAGOS, AKOKA, LAGOS STATE, NIGERIA.
JOSEPHINE NNEAMAKA ONYEKA-UBAKA DEPARTMENT OF STATISTICS, UNIVERSITY OF LAGOS, AKOKA, LAGOS STATE, NIGERIA

Keywords: Hidden Markov, Observable variable, Unobservable variable, Regime-switching, Distinct probability, Regression model

Abstract

Hidden Markov Models are used to study occurrences where a portion of the phenomenon is observable while the rest is unobservable. The model consists of two sets of random variables, namely, unobservable and observable random variables. Markov models are usually used to model the unobservable variable part of the hidden Markov model; a time-series regression model is used to model the observable part of the model. Then, the two random variables produce a regime-switching model known as the Markov-switching dynamic regression model with a distinct probability distribution. The parameters of this resulting model can be estimated using the maximum likelihood estimation method, and the characteristics of the regression model vary with the presiding regime of the model. The regression objective of this work is to explain the variability in the Nigerian monthly inflation rates using the variability in the average monthly United States dollar exchange rates. The correlation between the two datasets is determined using the least squares regression model and the Markov switching dynamic regression model. The Markov switching regression (Regime 2) model represents the high-variance regime. It explains the regression objectives more than the OLS regression model, as shown in the results. Consequently, it shows that when the Markov state model is in the high variance regime, Nigeria's economy shows a recession. The results depict that the regime-switching model outperformed the single regime model in capturing the properties of the data from the comparative analysis.

References

[1] K. Chung-Ming. Lecture on the Markov switching model. Institute of Economics Academia Sinica. https://www.sinica.edu.tw/as/ssrc/ckuan. (2002).
[2] D. Jurafsky and J.H. Martin. Speech and Language Processing. https://www.stanford.edu. (2021).
[3] B. Mor, S. Garhwal, Ajay Kumar. A systematic review of hidden Markov models and their applications. Archives of Computational Methods in Engineering. 3(2020) 1429-1448.
[4] P. Pomorski and D. Gorse. Improving on the Markov-Switching Regression Model by the Use of an Adaptive Moving Average. Computational Engineering, Finance, and Science. https://doi.org/10.48550/arXiv.2208.11574(2022).
[5] M. T. Kartal, F. Ayhan and D. Kirikkaleli. Regime-switching effect of COVID-19 pandemic on stock market index: evidence from Turkey as an emerging market example. Macroeconomics and Finance in Emerging Market Economies. https://doi.org/10.1080/17520843.2022.2091825(2022).
[6] D. Zivkov, J. Duraskovic and S. Manic. How do oil price changes affect inflation in Central and Eastern European countries? A waveletbased Markov switching approach. Baltic Journal of Economics. 19(1)(2019) 84-104.
[7] S. G. Tesfamichael and Y. A. Shiferaw. A Markov regime- switching regression approach to modelling NDVI from surface temperature and soil moisture. International Journal of Remote Sensing. 40(24)(2019) 9352-9379.
[8] G. Costa and R. H. Kwon. Risk parity portfolio optimization under a Markov regime-switching framework. Quantitative Finance. 19(3)(2019) 453-471.
[9] R. Alvarez, M. Camacho and M. Ruiz. Inference on Filtered and Smoothed Probabilities in Markov-Switching Autoregressive Models. Journal of Business & Economic Statistics. 37(3)(2019).
[10] K. Carstensen, M. Heinrich , M. Reif , M. H. Wolters. Predicting ordinary and severe recessions with a three-state Markov-switching dynamic factor model: An application to the German business cycle. International Journal of Forecasting. 36(3)(2020) 829-850.
[11] V. Moutinho, H. Oliveira, J. Mota. Examining the long term relationships between energy commodities prices and carbon prices on electricity prices using Markov switching regression. Energy Reports. 8 (2022) 589–594.
[12]Y. Kim, L. Huo and T.H. Kim. Dealing with Markov-switching parameters in quantile regression models. Communications in Statistics: Simulation and Computation. 51(11)(2022) 6773 - 6791.
[13] J. Stillwagon and P. Sullivan. Markov switching in exchange rate models: will more regimes help?. Empirical Economics. 59 (2020) 413 - 436.
[14] S.T. Hwu, C. J. Kim, and J. Piger. An N-State Endogenous Markov-Switching Model With Applications In Macroeconomics And Finance. Macroeconomic Dynamics. Cambridge University Press, 25(8)(2021) 1937-1965.
[15] T. Adam, A. Mayr, and T. Kneib. Gradient boosting in Markov-switching generalized additive models for location, scale, and shape. Econometrics and Statistics. 22 (2022) 3-16.
[16] A. Rahman, M. A. Khan, and L.Charfeddine. Financial development-economic growth nexus in Pakistan: new evidence from the Markov switching model. Cogent Economics & Finance. 8(1)(2020).
[17] M. K. Anser, D.I. Godil, M.A. Khan, A.A. Nassani, K. Zaman, and M. M. Q. Abro. The impact of coal combustion, nitrous oxide emissions, and traffic emissions on COVID-19 cases: a Markov-switching approach. Enviromental Science and Pollution Research. 28(2021) 64882–64891.
[18] M.I. Shah, D. Kirikkaleli, F. F. Adedoyin. Regime switching effect of COVID-19 pandemic on renewable electricity generation in Denmark. Renewable Energy. 175 (2021) 797-806.
[19] D. Degras, C. M. Ting, and H. Ombao. Markov-switching state-space models with applications to neuroimaging. Computational Statistics & Data Analysis. 174(2022).
[20] D. Sachin. A Math Lover’s Guide to Hidden Markov Models. https://www. towards datascience.com (2021a).
[21] D. Sachin. A worm’s eye-view of the Markov switching dynamic regression model. https://www.towards datascience.com (2021b).
[22] A. Ibn. Introduction to Markov Regime Switching Model. https://www.rpubs.com (2016).